# Thread: Proving the existence of a solution

1. ## Proving the existence of a solution

I have this equation: $x+2arctg(x)+4 = 0$

And I need to prove this equation has a real solution and find its approximation with two digits after the point.

As for the second part I know there is a formula. But I'm sure how to attempt to solve the first part. I think it has something to do with checking the slope at two points and showing that goes up or down between them (which by the look of the equation is probably true), but I'm not sure how exactly.

2. Well, the LHS is a continuous function on its domain. Suppose you were to find two values in the domain such that the LHS is negative at one value, and positive at the other value. What could you say then?